Introduction to R

• Background to R
• Data types in R
• Reading and writing data in R
• Plotting in R
• Statistics in R

R is scripting language and environment for statistical computing.

Developed by Robert Gentleman and Ross Ihaka.

Inheriting much from its predecessor S (Bell labs).

• Suited to high level data analysis
• Open source & cross platform
• Extensive graphics capabilities
• Diverse range of add-on packages
• Active community of developers
• Thorough documentation

• Simple calculations
• Variables
• Vectors
• Lists
• Matrices
• Data frames

At its most basic, R can be used as a simple calculator.

> 3+1

[1] 4

> 2*2

[1] 4

> sqrt(25)-1

[1] 4

The sqrt(25) demostrates the use of functions in R. A function performs a complex operation on it's arguments and returns the result.

In R, arguments are provided to a function within the parenthesis – ( ) – that follows the function name. So sqrt(ARGUMENT) will provide the square root of the value of ARGUMENT.

Other examples of functions include mean(), sum(), max().

Note multiple arguments are separated by a comma.

mean(2,4,6)

[1] 2

sum(2,4,6)

[1] 12

max(2,4,6)

[1] 6

R has many useful functions “built in” and ready to use as soon as R is loaded.

An incomplete, illustrative list can be seen here

In addition to R standard functions, additional functionality can be loaded into R using libraries. These include specialised tools for areas such as sequence alignment, read counting etc.

If you need to see how a function works try ? in front of the function name.

?sqrt

Lets run ?sqrt in RStudio and look at the help.

With functions such as mean() and sqrt(), the arguments to be provided are obvious and the order of these arguments doesnt matter.

mean(5,4,6)

[1] 5

mean(6,4,5)

[1] 6

Many functions however have an order to their arguments. Try and look at the arguments for the dir() function.

?dir

Often we know the names of arguments but not necessarily their order. In cases where we want to be sure we specify the right argument, we provide names for the arguments used.

dir()
dir(full.names=T)

This also means we don't have to copy out all the defaults for arguments preceeding it.

dir(full.names=T)
# Is equivalent to...
dir(".",NULL,FALSE,T)

As with other programming languages and even graphical calculators, R makes use of variables.

A variable stores a value as a letter or word.

In R, we make use of the assignment operator <-

x <- 10

Now x holds the value of 10

x

[1] 10

x

[1] 10

Variables can be altered in place

x <- 20
x

[1] 20

Variables can be used just as the values they contain.

x + sqrt(25)

[1] 25

Variables can be used to create new variables

y <- x + sqrt(25)
y

[1] 25

In R the most basic variable or data type is a vector. A vector is an ordered collection of values. The x and y variables we have previously assigned are examples of a vector of length 1.

x

[1] 20

length(x)

[1] 1

To create a multiple value vector we use the function c() to combine the supplied arguments into one vector.

x <- c(1,2,3,4,5,6,7,8,9,10)
x

 [1]  1  2  3  4  5  6  7  8  9 10

length(x)

[1] 10

Vectors of continuous stretches of values can be created by the shortcut - :

y <- 6:10
y

[1]  6  7  8  9 10

Other useful function to create stretchs of numeric vectors are seq() and rep(). The seq() function creates a sequence of numeric values from a specified start and end value, incrementing by a user defined amount. The rep() function repeats a variable a user-defined number of times.

seq(from=1,to=5,by=2)

[1] 1 3 5

rep(c(1,5,10),3)

[1]  1  5 10  1  5 10  1  5 10

Square brackets [] identify the position within a vector (the index). These indices can be used to extract relevant values from vectors.

x

 [1]  1  2  3  4  5  6  7  8  9 10

x[1]

[1] 1

x[8]

[1] 8

indices can be used to extract values from a multiple positions within a vector.

x[c(1,6)]

[1] 1 6

Negative indices can be used to extract all positions except that specified

x[-5]

[1]  1  2  3  4  6  7  8  9 10

We can use indices to modify a specific position in vector

x

 [1]  1  2  3  4  5  6  7  8  9 10

x[5] <- -5
x

 [1]  1  2  3  4 -5  6  7  8  9 10

Indices can be specified using other vectors.

y

[1]  6  7  8  9 10

x[y] <- 0
x

 [1]  1  2  3  4 -5  0  0  0  0  0

Square brackets [] for indexing

x[1]

[1] 1

Parentheses () for function argments.

sqrt(4)

[1] 2

Vectors in R can be used in arithmetic operations as seen with variables earlier. When a standard arithmetic operation is applied to vector, the operation is applied to each position in a vector.

x <- c(1,2,3,4,5,6,7,8,9,10)
x

 [1]  1  2  3  4  5  6  7  8  9 10

y <- x*2
y

 [1]  2  4  6  8 10 12 14 16 18 20

Multiple vectors can be used within arithmetic operations.

x+y

 [1]  3  6  9 12 15 18 21 24 27 30

When applying an arithmetic operation between two vectors of unequal length, the shorter will be recycled.

x+c(1,2)

 [1]  2  4  4  6  6  8  8 10 10 12

x+c(1,2,3)

 [1]  2  4  6  5  7  9  8 10 12 11

So far we have only looked at numeric vectors.

In R we can also create character vectors again using c() function. These vectors can be indexed just the same.

y <- c("ICTEM","CommonWealth","Wolfson")
y[2]

[1] "CommonWealth"

Character vectors can be used to assign names to other vectors.

x <- c(1:3)
names(x) <- y
x

       ICTEM CommonWealth      Wolfson 
           1            2            3 

These named vectors maybe indexed by a position's “name”.

x[c("ICTEM","Wolfson")]

  ICTEM Wolfson 
      1       3 

Index names missing from vectors will return special value “NA”

x[c("Strand")]

<NA> 
  NA 

In R, like many languages, when a value in a variable is missing, the value is assigned a NA value.

Similarly, when a calculation can not be perfomed, R will input a NaN value.

• NA - Not Available.
• NaN - Not A Number.

NA values allow for R to handle missing data correctly but requires different handling than standard numeric or character values. We will discuss handling NA values later.

The unique() function can be used to retrieve all unique character values from a character vector.

geneList <- c("Gene1","Gene2","Gene3","Gene4","Gene5","Gene1","Gene3")
unique(geneList)

[1] "Gene1" "Gene2" "Gene3" "Gene4" "Gene5"

A common task in R is to subset one character vector by another character vector.

The %in% operator can be used to subset the values within one character vector by those characters which are present in a second vectpr.

geneList <- c("Gene1","Gene2","Gene3","Gene4","Gene5","Gene1","Gene3")
secondGeneList <- c("Gene5","Gene3")
geneList[geneList %in% secondGeneList]

[1] "Gene3" "Gene5" "Gene3"

Logical vectors are a special type of vector made up of TRUE/T or FALSE/F boolean values.

z <- c(T,F,T,F,T,F,T,F,T,F) 
# z <-  c(TRUE,FALSE,TRUE,FALSE,TRUE,FALSE,TRUE,FALSE,TRUE,FALSE) 
z

 [1]  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE

Logical vectors can be used like an index to specify postions in a vector. TRUE values will return that corresponding position in the vector being indexed.

x <- 1:10
x[z]

[1] 1 3 5 7 9

Other vectors may be evaluated to produce logical vectors. This can be very useful when using a logical to index.

Common examples are:

• == evaluates as equal.
• > and < evaluates as greater or less than respectively.
• >= and <= evaluates as greater than or equal or less than or equal respectively.

x > 5

 [1] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE

x[x > 5]

[1]  6  7  8  9 10

Logical vectors can be used in combination in order to index vectors. To combine logical vectors we can use some common R operators.

• & Requires both logical operators to be TRUE
• | Requires either logical operators to be TRUE.
• ! Reverses logical operator, so TRUE is FALSE and FALSE is TRUE.

x <- 1:10
!x > 4

 [1]  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE

x > 4 & x < 7

 [1] FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE

x > 4 | x < 7

 [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

Such combinations can allow for complex selection of vector's values.

x <- 1:10
x[x > 4 & x < 7]

[1] 5 6

x[x > 4 & !x < 7]

[1]  7  8  9 10

Exercise on vectors can be found here

Answers can be found here here

In programs such as Excel, we are used to tables.

All progamming languages have a concept of a table. In R, the most basic table type is a matrix.

A Matrix can be created using the matrix() function with the arguments of nrow and ncol specifying the number of rows and columns respectively.

narrowMatrix <- matrix(1:10, nrow=5, ncol=2)
narrowMatrix

     [,1] [,2]
[1,]    1    6
[2,]    2    7
[3,]    3    8
[4,]    4    9
[5,]    5   10

wideMatrix <- matrix(1:10, nrow=2, ncol=5)
wideMatrix

     [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

To find dimensions of a matrix, the dim() function will provide dimensions as row number and column number while nrow() and ncol() will return just row number and column number respectively.

dim(narrowMatrix)

[1] 5 2

nrow(narrowMatrix)

[1] 5

ncol(narrowMatrix)

[1] 2

As with vectors, matrices can be named. For matrices the naming is done by columns and rows using colnames() and rownames() functions.

namedMatrix <- matrix(1:10,ncol=5,nrow=2)
colnames(namedMatrix) <- paste("Column",1:5,sep="_")
rownames(namedMatrix) <- paste("Row",1:2,sep="_")
namedMatrix

      Column_1 Column_2 Column_3 Column_4 Column_5
Row_1        1        3        5        7        9
Row_2        2        4        6        8       10

Information on matrix names can also be retreived using the same functions.

colnames(namedMatrix)

[1] "Column_1" "Column_2" "Column_3" "Column_4" "Column_5"

rownames(namedMatrix)

[1] "Row_1" "Row_2"

Selecting and replacing portions of a matrix can be done by indexing using square brackets [] much like for vectors.

When indexing matrices, two values may be provided within the square brackets separated by a comma to retrieve information on a matrix position.

The first value(s) corresponds to row(s) and the second to column(s).

• myMatrix[rowOfInterest,columnOfInterest]

narrowMatrix

     [,1] [,2]
[1,]    1    6
[2,]    2    7
[3,]    3    8
[4,]    4    9
[5,]    5   10

Value of first column, second row

narrowMatrix[2,1]

[1] 2

Similarly, whole rows or columns can be extracted. Single rows and columns will return a vector. When multiple columns or row indices are specified, a matrix is returned.

Values of second column (row index is empty!)

narrowMatrix[,2]

[1]  6  7  8  9 10

Values of third row (column index is empty!)

narrowMatrix[3,]

[1] 3 8

Values of second and third row (column index is empty!)

narrowMatrix[c(2,3),]

     [,1] [,2]
[1,]    2    7
[2,]    3    8

As with vectors, names can be used for indexing when present

colnames(narrowMatrix) <- paste("Column",1:2,sep="_")
rownames(narrowMatrix) <- paste("Row",1:5,sep="_")
narrowMatrix[,"Column_1"]

Row_1 Row_2 Row_3 Row_4 Row_5 
    1     2     3     4     5 

narrowMatrix["Row_1",]

Column_1 Column_2 
       1        6 

narrowMatrix[,"Column_1"]

Row_1 Row_2 Row_3 Row_4 Row_5 
    1     2     3     4     5 

narrowMatrix["Row_1","Column_1"]

[1] 1

As with vectors, matrices can have arithmetic operations applied to cells,rows, columns or the whole matrix

narrowMatrix

      Column_1 Column_2
Row_1        1        6
Row_2        2        7
Row_3        3        8
Row_4        4        9
Row_5        5       10

narrowMatrix[1,1]+2

[1] 3

narrowMatrix[1,]+2

Column_1 Column_2 
       3        8 

mean(narrowMatrix)

[1] 5.5

As with vectors, matrices can have their elements replaced

narrowMatrix

      Column_1 Column_2
Row_1        1        6
Row_2        2        7
Row_3        3        8
Row_4        4        9
Row_5        5       10

narrowMatrix[1,1] <- 10
narrowMatrix[,2] <- 1
narrowMatrix

      Column_1 Column_2
Row_1       10        1
Row_2        2        1
Row_3        3        1
Row_4        4        1
Row_5        5        1

matrices must be all one type (numeric or character).

Here replacing one value with character will turn numeric matrix to character matrix.

narrowMatrix[,2] *2

Row_1 Row_2 Row_3 Row_4 Row_5 
    2     2     2     2     2 

narrowMatrix[1,1] <- "Not_A_Number"
narrowMatrix

      Column_1       Column_2
Row_1 "Not_A_Number" "1"     
Row_2 "2"            "1"     
Row_3 "3"            "1"     
Row_4 "4"            "1"     
Row_5 "5"            "1"     

narrowMatrix[,2] *2

Error in narrowMatrix[, 2] * 2: non-numeric argument to binary operator

Exercise on vectors can be found here

Answers can be found here here

A special case of a vector is a factor.

Factors are used to store data which may be grouped in categories (categorical data). Specifying data as categorical allows R to properly handle the data and make use of functions specific to categorical data.

To create a factor from a vector we use the factor() function. Note that the factor now has an additional component called “levels” which identifies all categories within the vector.

vectorExample <- c("male","female","female","female")
factorExample <- factor(vectorExample)
factorExample

[1] male   female female female
Levels: female male

levels(factorExample)

[1] "female" "male"  

An example of the use of levels can be seen from applying the summary() function to the vector and factor examples

summary(vectorExample)

   Length     Class      Mode 
        4 character character 

summary(factorExample)

female   male 
     3      1 

In our factor example, the levels have been displayed in an alphabetical order. To adjust the display order of levels in a factor, we can supply the desired display order to levels argument in the factor() function call.

factorExample <- factor(vectorExample,levels=c("male","female"))
factorExample

[1] male   female female female
Levels: male female

summary(factorExample)

  male female 
     1      3 

In some cases there is no natural order to the categories such that one category is greater than the other (nominal data). In this case we can see that R is gender neutral.

factorExample <- factor(vectorExample,levels=c("male","female"))
factorExample[1] < factorExample[2]

[1] NA

In other cases there will be a natural ordering to the categories (ordinal data). A factor can be specified to be ordered using the ordered argument in combination with specified levels argument.

factorExample <- factor(c("small","big","big","small"),ordered=TRUE,levels=c("small","big"))
factorExample[1] < factorExample[2]

[1] TRUE

Unlike vectors, replacing elements within a factor isn't so easy. While replacing one element with an established level is possible, replacing with a novel element will result in a warning.

factorExample <- factor(c("small","big","big","small"))
factorExample[1] <- c("big")
factorExample

[1] big   big   big   small
Levels: big small

factorExample[1] <- c("huge")
factorExample

[1] <NA>  big   big   small
Levels: big small

To add a new level we can use the levels argument.

levels(factorExample) <- c("big","small","huge")
factorExample[1] <- c("huge")
factorExample

[1] huge  big   big   small
Levels: big small huge

We saw that with matrices you can only have one type of data. We tried to create a matrix with a character element and the entire matrix became a character.

In practice, we would want to have a table which is a mixture of types (e.g a table with sample names (character), sample type (factor) and survival time (numeric))

In R, we make use of the data.frame object which allows us to store tables with columns of different data types. To create a data frame we can simply use the data.frame() function.

patientName <- c("patient1","patient2","patient3","patient4")
patientType <- factor(rep(c("male","female"),2))
survivalTime <- c(1,30,2,20)
dfExample <- data.frame(Name=patientName, Type=patientType,Survival_Time=survivalTime)
dfExample

      Name   Type Survival_Time
1 patient1   male             1
2 patient2 female            30
3 patient3   male             2
4 patient4 female            20

Data frames may be indexed just as matrices.

dfExample

      Name   Type Survival_Time
1 patient1   male             1
2 patient2 female            30
3 patient3   male             2
4 patient4 female            20

dfExample[dfExample[,"Survival_Time"] > 10,]

      Name   Type Survival_Time
2 patient2 female            30
4 patient4 female            20

Unlike matrices, it is possible to index a column by using the $ symbol.

dfExample <- data.frame(Name=patientName,Type=patientType,Survival_Time=survivalTime)
dfExample$Survival_Time

[1]  1 30  2 20

dfExample[dfExample$Survival_Time < 10,]

      Name Type Survival_Time
1 patient1 male             1
3 patient3 male             2

Using the $ allows for R to autocomplete your selection and so can speed up coding.

dfExample$Surv

[1]  1 30  2 20

But this will not work..

dfExample[,"Surv"]

The $ operator also allows for the creation of new columns for a data frame on the fly.

dfExample

      Name   Type Survival_Time
1 patient1   male             1
2 patient2 female            30
3 patient3   male             2
4 patient4 female            20

dfExample$newColumn <- rep("newData",nrow(dfExample))
dfExample

      Name   Type Survival_Time newColumn
1 patient1   male             1   newData
2 patient2 female            30   newData
3 patient3   male             2   newData
4 patient4 female            20   newData

Certain columns can not be replaced in data frames. Numeric columns may have their values replaced but columns with character values may not by default. This occurs because character vectors are treated as factors by default.

dfExample[dfExample[,"Survival_Time"] < 10,"Survival_Time"] <- 0
dfExample

      Name   Type Survival_Time newColumn
1 patient1   male             0   newData
2 patient2 female            30   newData
3 patient3   male             0   newData
4 patient4 female            20   newData

dfExample[dfExample[,"Survival_Time"] < 10,"Name"] <- "patientX"
dfExample

      Name   Type Survival_Time newColumn
1     <NA>   male             0   newData
2 patient2 female            30   newData
3     <NA>   male             0   newData
4 patient4 female            20   newData

It is possible to update factors in data.frames just as with standard factorss

dfExample <- data.frame(Name=patientName,Type=patientType,Survival_Time=survivalTime)

levels(dfExample[,"Name"]) <- c(levels(dfExample[,"Name"]) , "patientX")
dfExample[dfExample[,"Survival_Time"] < 10,"Name"] <- "patientX"
dfExample

      Name   Type Survival_Time
1 patientX   male             1
2 patient2 female            30
3 patientX   male             2
4 patient4 female            20

If you wish to avoid using factors in data.frames then the stringsAsFactors argument to data.frame() function should be set to FALSE

dfExample <- data.frame(Name=patientName,
                        Type=patientType,
                        Survival_Time=survivalTime,
                        stringsAsFactors = F)

levels(dfExample[,"Name"]) <- c(levels(dfExample[,"Name"]) , "patientX")
dfExample[dfExample[,"Survival_Time"] < 10,"Name"] <- "patientX"
dfExample

      Name   Type Survival_Time
1 patientX   male             1
2 patient2 female            30
3 patientX   male             2
4 patient4 female            20

A useful function in R is order()

For numeric vectors, order() by default returns the indices of a vector in that vector's increasing order. This behaviour can be altered by using the “decreasing” argument passed to order.

testOrder <- c(2,1,3)
testOrder

[1] 2 1 3

testOrder[order(testOrder)]

[1] 1 2 3

testOrder[order(testOrder,decreasing=T)]

[1] 3 2 1

When a vector contains NA values, these NA values will, by default, be placed last in ordering indices. This can be controlled by na.last argument.

testOrder <- c(2,1,NA,3)
testOrder[order(testOrder,decreasing=T,na.last=T)]

[1]  3  2  1 NA

testOrder[order(testOrder,decreasing=T,na.last=F)]

[1] NA  3  2  1

To do this we can use the merge() function with the data frames as the first two arguments. We can then specify the columns to merge by with the by argument. To keep only data pertaining to values common to both data frames the all argument is set to TRUE.

mergedDF <- merge(dfExample,dfExample2,by=1,all=F)
mergedDF

      Name   Type Survival_Time height
1 patient1   male             1    6.1
2 patient2 female            30    5.1
3 patient3   male             2    5.5

Exercise on data frames and factors can be found here

Answers can data frames and factorsbe found here here

Lists are the final data-type we will look at.

In R, lists provide a general container which may hold any data types of unequal lengths as part of its elements. To create a list we can simply use the list() function with arguments specifying the data we wish to include in the list.

firstElement <- c(1,2,3,4)
secondElement <- matrix(1:10,nrow=2,ncol=5)
thirdElement <- data.frame(colOne=c(1,2,4,5),colTwo=c("One","Two","Three","Four"))
myList <- list(firstElement,secondElement,thirdElement)
myList

[[1]]
[1] 1 2 3 4

[[2]]
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

[[3]]
  colOne colTwo
1      1    One
2      2    Two
3      4  Three
4      5   Four

Just as with vectors, list elements can be assigned names.

myNamedList <- list(First=firstElement,Second=secondElement,Third=thirdElement)
myNamedList

$First
[1] 1 2 3 4

$Second
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

$Third
  colOne colTwo
1      1    One
2      2    Two
3      4  Three
4      5   Four

List, as with other data types in R can be indexed. In contrast to other types, using [] on a list will subset the list to another list of selected indices. To retrieve an element from a list in R , two square brackets [[]] must be used.

myList <- list(firstElement,secondElement,thirdElement)
myList[1]

[[1]]
[1] 1 2 3 4

myList[[1]]

[1] 1 2 3 4

As with data.frames, the $ sign may be used to extract elements from a list

myNamedList$First

[1] 1 2 3 4

Again, similar to vectors, lists can be joined together in R using the c() function

myNamedList <- list(First=firstElement,Second=secondElement,Third=thirdElement)
myNamedList <- c(myNamedList,list(fourth=c(4,4)))
myNamedList[c(1,4)]

$First
[1] 1 2 3 4

$fourth
[1] 4 4

Note that on last slide we are joining two lists. If we joined a vector to a list, all elements of the vector would become list elements.

myList <- c(myList,c(4,4))
myList

[[1]]
[1] 1 2 3 4

[[2]]
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

[[3]]
  colOne colTwo
1      1    One
2      2    Two
3      4  Three
4      5   Four

[[4]]
[1] 4

[[5]]
[1] 4

Sometimes you will wish to “flatten” out a list. When a list contains compatable objects, i.e. list of all one type, the unlist() function can be used. Note the maintenance of names with their additional sufficies.

myNamedList <- list(First=c(1,2,3),Second=c(2,6,7),Third=c(1,4,7))
myNamedList

$First
[1] 1 2 3

$Second
[1] 2 6 7

$Third
[1] 1 4 7

flatList <- unlist(myNamedList)
flatList[1:7]

 First1  First2  First3 Second1 Second2 Second3  Third1 
      1       2       3       2       6       7       1 

A common step is to turn a list of standard results into matrix. This can be done in a few steps in R.

myNamedList <- list(First=c(1,2,3),Second=c(2,6,7),Third=c(1,4,7))
flatList <- unlist(myNamedList)
listAsMat <- matrix(flatList,
                    nrow=length(myNamedList),
                    ncol=3,
                    byrow=T,
                    dimnames=list(names(myNamedList)))
listAsMat

       [,1] [,2] [,3]
First     1    2    3
Second    2    6    7
Third     1    4    7

Most of the time, you will not be generating data in R but will be importing data from external files.

A standard format for this data is a table

Tables from text files can be read with read.table() function

Table <- read.table("data/readThisTable.csv",sep=",",header=T)
Table[1:4,1:3]

  Gene_Name Sample_1.hi Sample_2.hi
1    Gene_a    4.570237    3.230467
2    Gene_b    3.561733    3.632285
3    Gene_c    3.797274    2.874462
4    Gene_d    3.398242    4.415202

Here we have provided two arguments.

• sep argument specifies how columns are separated in our text file. (“,” for .csv, “\t” for .tsv)
• header argument specifies whether columns have headers.

read.table() allows for significant control over reading files through its many arguments. Have a look at options by using ?read.table

The row.names argument can be used to specify a column to use as row names for the resulting data frame. Here we use the first column as row names.

Table <- read.table("data/readThisTable.csv",sep=",",header=T,row.names=1)
Table[1:4,1:3]

       Sample_1.hi Sample_2.hi Sample_3.hi
Gene_a    4.570237    3.230467    3.351827
Gene_b    3.561733    3.632285    3.587523
Gene_c    3.797274    2.874462    4.016916
Gene_d    3.398242    4.415202    4.893561

As mentioned, data which is read into R through read.table() will be of data frame class.

To avoid character columns being converted into factors, we can specify the stringsAsFactors argument here.

Table <- read.table("data/readThisTable.csv",sep=",",header=T,stringsAsFactors=F)

Other very useful functions for read table include:

• skip - To set number of lines to skip when reading.
• comment.char - To set the start identifier for lines not to be read.

The read.table function can also read data from http.

URL <- "http://mrccsc.github.io/readThisTable.csv"
Table <- read.table(URL,sep=",",header=T)
Table[1:2,1:3]

  Gene_Name Sample_1.hi Sample_2.hi
1    Gene_a    4.111851    3.837018
2    Gene_b    6.047822    5.683518

And the clipboard.(This is Windows version)

Table <- read.table(file="clipboard",sep=",",header=T)

read.table() function will by default read every row and column of a file.

The scan() function allows for the selection of particular columns to be read into R and so can save memory when files are large.

x <- scan("data/readThisTable.csv",sep=",",
what = c(list(""),rep(list(NULL), 6)),skip=1)
x[1:3]

[[1]]
[1] "Gene_a" "Gene_b" "Gene_c" "Gene_d" "Gene_e" "Gene_f" "Gene_g" "Gene_h"

[[2]]
NULL

[[3]]
NULL

Once we have our data analysed in R, we will want to export it to a file.

The most common method is to use the write.table() function

write.table(Table,file="data/writeThisTable.csv",sep=",")

Since our data has column names but no row names, I will provide the arguments col.names and row.names to write.table()

write.table(Table,file="data/writeThisTable.csv", sep=",", row.names =F,col.names=T)

R has excellent graphics and plotting capabilities. They are mostly found in following three sources.

• base graphics
• the lattice package
• the ggplot2 package

Lattice and ggplot2 packages are built on grid graphics package while the base graphics routines adopt a pen and paper model for plotting.

• Line Charts

First we'll produce a very simple graph using the values in the treatment vector:

treatment <- c(0.02,1.8, 17.5, 55,75.7, 80)

Plot the treatment vector with default parameters

plot(treatment)

Bar Charts Let's start with a simple bar chart graphing the treatment vector: Plot treatment

barplot(treatment)

R makes it easy to combine multiple plots into one overall graph, using either the par( ) or layout( ) function. With the par( ) function, you can include the option mfrow=c(nrows, ncols) to create a matrix of nrows x ncols plots that are filled in by row. mfcol=c(nrows, ncols) fills in the matrix by columns.

Define a layout with 2 rows and 2 columns

par(mfrow=c(2,2))

There are many different ways of saving your plots in R.

The only argument you would need is name of file in which you want to save the plot.

Plotting commands then can be entered as usual. The output would be redirected to the file.

When you're done with your plotting commands, enter the dev.off() command.

bmp(filename, width = 480, height = 480, units = "px", point-size = 12)
jpeg(filename, width = 480, height = 480, units = "px", point-size = 12, quality = 75)

Lattice is an excellent package for visualizing multivariate data. It has great set of routines for quickly displaying complex data sets with ease.

Advantages of using lattice package are as following.

Plots with lattice package usually look better.

They can be extended in powerful ways.

The resulting output can be annotated, edited and saved.

Let's look at how to create a scatterplot in ggplot2. We'll use the iris data frame that's automatically loaded into R. What does the data frame contain? We can use the head function to look at the first few rows

head(iris, n = 3)  

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa

In the scatterplot examples above, we implicitly used a point geom, the default when you supply two arguments to qplot(). These two invocations are equivalent.

qplot(Sepal.Length, Petal.Length, data = iris, geom = "point")
qplot(Sepal.Length, Petal.Length, data = iris)

But we can also easily use other types of geoms to create more kinds of plots. Barcharts: geom = “bar”

qplot(Sepal.Length, Petal.Length, data = iris, geom = "line", color = Species) 

Orange is another built-in data frame that describes the growth of orange trees.

qplot(age, circumference, data = Orange, geom = "line", colour = Tree,
    main = "How does orange tree circumference vary with age?")

We can also plot both points and lines.

qplot(age, circumference, data = Orange, geom = c("point", "line"), colour = Tree)

R has a powerful set of statistical methods. Including:

• Standard statistical tests
• Statistical modelling
• Further methods available in add on packages

One of the simplest statistical tools are summary() and table(). These functions provide descriptive statistics for data frames and character vectors or factors.

patientName <- c("patient1","patient2","patient3","patient4")
patientType <- factor(rep(c("male","female"),2))
survivalTime <- c(1,30,2,20)
dfExample <- data.frame(Name=patientName,Type=patientType,Survival_Time=survivalTime)

The table() provides a breakdown of frequency of occurrence of all unique values in vector or factor.

table(patientType)

patientType
female   male 
     2      2 

summary() provides a breakdown of occurrence for all character or factor columns and min,max,mean and quantiles for numeric columns.

summary(dfExample)

       Name       Type   Survival_Time  
 patient1:1   female:2   Min.   : 1.00  
 patient2:1   male  :2   1st Qu.: 1.75  
 patient3:1              Median :11.00  
 patient4:1              Mean   :13.25  
                         3rd Qu.:22.50  
                         Max.   :30.00  

The table() function can be used to generate frequency tables across data.frames.

table(dfExample)

, , Survival_Time = 1

          Type
Name       female male
  patient1      0    1
  patient2      0    0
  patient3      0    0
  patient4      0    0

, , Survival_Time = 2

          Type
Name       female male
  patient1      0    0
  patient2      0    0
  patient3      0    1
  patient4      0    0

, , Survival_Time = 20

          Type
Name       female male
  patient1      0    0
  patient2      0    0
  patient3      0    0
  patient4      1    0

, , Survival_Time = 30

          Type
Name       female male
  patient1      0    0
  patient2      1    0
  patient3      0    0
  patient4      0    0

ftable() function provides a method to generate or print the results from table() in a neater format.

ftable(dfExample)

                Survival_Time 1 2 20 30
Name     Type                          
patient1 female               0 0  0  0
         male                 1 0  0  0
patient2 female               0 0  0  1
         male                 0 0  0  0
patient3 female               0 0  0  0
         male                 0 1  0  0
patient4 female               0 0  1  0
         male                 0 0  0  0

A common task in statistical analysis is to investigate the relationship between pairs of numeric vectors.

This can be done by identifying the correlation between numeric vectors using the cor() function in R.

In this example we use cor() to identify the pearson between two variables. The method argument may be set to make use of different correlation methods.

• Perfectly posively correlated vectors will return 1
• Perfectly negatively correlated vectors will return -1
• Vectors showing no or little correlation will be close to 0.

Often we wish to apply correlation analysis to all columns or rows in a matrix in a pair-wise manner. To do this in R, we can simply pass the cor() function a single argument of the numeric matrix of interest. The cor() function will then perform all pair-wise correlations between columns.

cor(minRep)[1:2,2:5]

            Sample_2.hi Sample_3.hi Sample_4.low Sample_5.low
Sample_1.hi    0.960208   0.9776501    0.1665599    0.3194427
Sample_2.hi    1.000000   0.9721985    0.1581274    0.2894231

Similar functions are available for other distibution types including:

• pbinom (binomial)
• pnbinom (negative binomial),
• phyper (hyper-geometric)
• pt (T distribution)

We can use rnorm to generate random values following a normal distribution. Here we produce 10 normally distributed numeric values with mean 8 and standard deviation of 3

rnorm(10,mean=8,sd=3)

 [1]  9.371843 11.494115  7.330717  3.594831 10.065677 10.329720  5.004292
 [8] 13.631312  9.582516  9.556455

We can also use these functions to interrogate values assuming a normal distribution for the data.

The probablity of a value being exactly 8 for a distribution of mean 8 and standard deviation 3.

dnorm(8,mean=8,sd=3)

[1] 0.1329808

The probablity of a value being less than 8 for a distribution of mean 8 and standard deviation 3.

pnorm(8,mean=8,sd=3)

[1] 0.5

The value for which i have a 50 percent being greater than given a normal distribution of mean 8 and standard deviation 3.

qnorm(0.5,mean=8,sd=3)

[1] 8

On top of descriptive statistics, R has several statistical tests covering a range of problems and data types.

Some of the most used tests of two samples include:

• var.test() - Comparing 2 variances (Fisher's F test)

• t.test() - Comparing 2 sample means with normal errors (Student's t-test)

• wilcox.test() - Comparing 2 means with non-normal errors (Wilcoxon's rank test)

• fisher.test() - Testing for independence of 2 variables in a contingency table (Fisher's exact test)

To perform a t-test we will read in some datasets, test that the variances of the datasets are equal and then perform the actual t-tests.

tTestExample <- read.table("data/tTestData.csv",sep=",",header=T)
tTestExample

          A        B        C
1  26.03199 40.65549 33.78191
2  27.00897 40.59726 39.48001
3  27.57468 39.86103 34.63261
4  27.15929 39.96254 42.62425
5  25.82156 42.54450 35.48016
6  26.18872 39.31856 40.49148
7  26.30709 40.80434 38.91200
8  26.21609 39.96368 40.74275
9  25.84095 40.08374 34.28705
10 26.86587 40.18931 37.80057

First we can specify the columsn of interest using $ and calculate their variance using var().

var(tTestExample$A)

[1] 0.367875

var(tTestExample$B)

[1] 0.7614086

var(tTestExample$C)

[1] 9.681179

Now we can test for any differences in variances between A and B and A and C with an F-test using the var.test() function.

var.test(tTestExample$A,tTestExample$B)

    F test to compare two variances

data:  tTestExample$A and tTestExample$B
F = 0.4832, num df = 9, denom df = 9, p-value = 0.2936
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.1200078 1.9451614
sample estimates:
ratio of variances 
         0.4831506 

var.test(tTestExample$A,tTestExample$C)

    F test to compare two variances

data:  tTestExample$A and tTestExample$C
F = 0.038, num df = 9, denom df = 9, p-value = 4.092e-05
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.009438411 0.152983699
sample estimates:
ratio of variances 
        0.03799899 

Now we know the structure and class of the htest object we can access the slots realting to information we want just as with a named list.

The p-value

result$p.value

[1] 0.293592

The statistic

result$statistic

        F 
0.4831506 

The data used in function call

result$data.name

[1] "tTestExample$A and tTestExample$B"

Now we have ascertained that GroupA and GroupB have similar variances. We can therefore perform a standard t-test to assess the significance of differences betweem the groups.

Result <- t.test(tTestExample$A,tTestExample$B,alternative ="two.sided", var.equal = T)
Result

    Two Sample t-test

data:  tTestExample$A and tTestExample$B
t = -41.3528, df = 18, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -14.60253 -13.19051
sample estimates:
mean of x mean of y 
 26.50152  40.39804 

To compare groups of unequal variance then the var.equal argument may be set to FALSE (which is the default).

Result <- t.test(tTestExample$A,tTestExample$C,alternative ="two.sided", var.equal = F)
Result

    Welch Two Sample t-test

data:  tTestExample$A and tTestExample$C
t = -11.2941, df = 9.683, p-value = 6.855e-07
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -13.56531  -9.07821
sample estimates:
mean of x mean of y 
 26.50152  37.82328 

The same result to that shown could be achieved by specifying a formula for the comparison. Here we wish to compare column A versus B so we could simply specify the formula and the data to be used.

longFrame <- data.frame(Group = c(rep("A",nrow(tTestExample)),rep("B",nrow(tTestExample))), Value=c(tTestExample$A,tTestExample$B))

result <- t.test(Value~Group,longFrame,alternative ="two.sided",
                 var.equal = T)
result

    Two Sample t-test

data:  Value by Group
t = -41.3528, df = 18, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -14.60253 -13.19051
sample estimates:
mean in group A mean in group B 
       26.50152        40.39804 

The lm() function fits a linear regression to your data and provides useful information on the generated fit.

In the example below we fit a linear model using lm() on the lmExample dataset with column Y as the dependent variable and column X as the explanatory variable.

> lmResult <- lm(Y~X,data=lmExample)
> lmResult

Call:
lm(formula = Y ~ X, data = lmExample)

Coefficients:
(Intercept)            X  
      7.001        1.972  

Printing the result from lm() shows the call to lm() and the coefficients including the intercept.

As we have seen, printing the model result provides the intercept and slope of line.

To get some more information on the model we can use the summary() function

> summary(lmResult)

Call:
lm(formula = Y ~ X, data = lmExample)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.0150 -2.3688 -0.2079  2.6068  5.0538 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  7.00053    0.93207   7.511 3.91e-13 ***
X            1.97218    0.01325 148.894  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.858 on 398 degrees of freedom
Multiple R-squared:  0.9824,    Adjusted R-squared:  0.9823 
F-statistic: 2.217e+04 on 1 and 398 DF,  p-value: < 2.2e-16

Call:
lm(formula = Y ~ X, data = lmExample)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.0150 -2.3688 -0.2079  2.6068  5.0538 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  7.00053    0.93207   7.511 3.91e-13 ***
X            1.97218    0.01325 148.894  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.858 on 398 degrees of freedom
Multiple R-squared:  0.9824,    Adjusted R-squared:  0.9823 
F-statistic: 2.217e+04 on 1 and 398 DF,  p-value: < 2.2e-16

The R-squared value represents the proportion of variability in the response variable that is explained by the explanatory variable.

A high R-squared here indicates that the line fits closely to the data.

> summary(lmResult)

Call:
lm(formula = Y ~ X, data = lmExample)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.0150 -2.3688 -0.2079  2.6068  5.0538 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  7.00053    0.93207   7.511 3.91e-13 ***
X            1.97218    0.01325 148.894  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.858 on 398 degrees of freedom
Multiple R-squared:  0.9824,    Adjusted R-squared:  0.9823 
F-statistic: 2.217e+04 on 1 and 398 DF,  p-value: < 2.2e-16

The results from linear models also provides a measure of significance for a variable not being relevant in Pr(>|t|) column. A low p-value suggests the variable is useful in prediction of the dependent variable.

Exercise on statistics can be found here

Answers can be found here here